On zero energy states in graphene

Abstract

We obtain zero energy states in graphene for a number of potentials and discuss the relation of the decoupled Schrödinger-like equations for the the spinor components with non relativistic $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics.

arXiv comment4 pages, 2 figures. Presentation improved, two figures added, references updated

References in corpus (18)

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Cited by in corpus (17)

• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• Construction of zero energy states in graphene through the supersymmetry formalism
• An analysis of the zero energy states in graphene
• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
• Conditional electron confinement in graphene via smooth magnetic fields
• Zero-energy vortices in Dirac materials
• New solutions for graphene with scalar potentials by means of generalized intertwining
• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• Generalized harmonic confinement of massless Dirac fermions in (2+ 1) dimensions
• Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
• Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Massive and massless two-dimensional Dirac particles in electric quantum dots
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Confinement in bilayer graphene via intra- and inter-layer interactions
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime